Question

Six different​ second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings​ (in mmHg) are listed below. Find the​ range, variance, and standard deviation for the given sample data. If the​ subject's blood pressure remains constant and the medical students correctly apply the same measurement​ technique, what should be the value of the standard​ deviation? 131 137 138 141 141 149131 137 138 141 141 149 Rangeequals=nothing mmHg Sample varianceequals=nothing mmHgsquared2 ​(Round to the nearest tenth as​ needed.) Sample standard deviationequals=nothing mmHg​ (Round to the nearest tenth as​ needed.) What should be the value of the standard​ deviation?

A. ​Ideally, the standard deviation would be one because all the measurements should be the same.
B. ​Ideally, the standard deviation would be zero because all the measurements should be the same.
C. ​Ideally, the standard deviation would be one because this is the lowest standard deviation that can be achieved.
D. There is no way to tell what the standard deviation should be.

Answer 1

`Range = 149-131=18`

`s^2 =((131-139.5)^2 +(137-139.5)^2 +(138-139.5)^2 +(141-139.5)^2 +(141-139.5)^2 +(149-139.5)^2)/(6-1)=35.1`
`s =√(35.1)=5.9`

B. ​Ideally, the standard deviation would be zero because all the measurements should be the same.

Explanation:

For this case we have the following data:

131 137 138 141 141 149

For this case the range is defined as
`Range = Max-Min`

And for our case we have
`Range = 149-131=18`

First we need to calculate the average given by this formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)=(837)/(6)=139.5`

We can calculate the sample variance with the following formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar x)^2)/(n-1)`

And if we replace we got:

`s^2 =((131-139.5)^2 +(137-139.5)^2 +(138-139.5)^2 +(141-139.5)^2 +(141-139.5)^2 +(149-139.5)^2)/(6-1)=35.1`

And the standard deviation is just the square root of the variance so then we got:

`s =√(35.1)=5.9`

If the​ subject's blood pressure remains constant and the medical students correctly apply the same measurement​ technique, what should be the value of the standard​ deviation?

For this case the variance and deviation should be 0 since we not evidence change then we not have variation. And for this case the best answer is:

B. ​Ideally, the standard deviation would be zero because all the measurements should be the same.